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CS221: Algorithms and Data Structures Lecture #3.5 Sorting Takes Priority Steve Wolfman 2011W2 1.

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Presentation on theme: "CS221: Algorithms and Data Structures Lecture #3.5 Sorting Takes Priority Steve Wolfman 2011W2 1."— Presentation transcript:

1 CS221: Algorithms and Data Structures Lecture #3.5 Sorting Takes Priority Steve Wolfman 2011W2 1

2 Today’s Outline Sorting with Priority Queues, Three Ways 2

3 Quick Review of Sorts Insertion Sort: Keep a list of already sorted elements. One by one, insert new elements into the right place in the sorted list. Selection Sort: Repeatedly find the smallest (or largest) element and put it in the next slot. Merge Sort: Divide the list in half, sort the halves, merge them back together. (Base case: length  1.) 3

4 How Do We Sort with a Priority Queue? You have a bunch of data. You want to sort by priority. You have a priority queue. WHAT DO YOU DO? 4 F(7) E(5) D(100) A(4) B(6) insert deleteMin G(9)C(3)

5 “PQSort” Sort(elts): pq = new PQ for each elt in elts: pq.insert(elt); sortedElts = new array of size elts.length for i = 0 to elts.length – 1: sortedElts[i] = pq.deleteMin return sortedElts 5 What sorting algorithm is this? a.Insertion Sort b.Selection Sort c.Heap Sort d.Merge Sort e.None of these

6 Reminder: Naïve Priority Q Data Structures Unsorted list: –insert: worst case O(1) –deleteMin: worst case O(n) Sorted list: –insert: worst case O(n) –deleteMin: worst case O(1) 6

7 “PQSort” deleteMaxes with Unsorted List MAX-PQ How long does inserting all of these elements take? And then the deletions…

8 “PQSort” deleteMaxes with Unsorted List MAX-PQ PQ

9 “PQSort” deleteMaxes with Unsorted List MAX-PQ PQ Result

10 “PQSort” deleteMaxes with Unsorted List MAX-PQ PQ Result PQResult

11 “PQSort” deleteMaxes with Unsorted List MAX-PQ PQ Result PQResult PQResult

12 Two PQSort Tricks 1)Use the array to store both your results and your PQ. No extra memory needed! 2)Use a max-heap to sort in increasing order (or a min-heap to sort in decreasing order) so your heap doesn’t “move” during deletions. 12

13 “PQSort” deleteMaxes with Unsorted List MAX-PQ How long does “build” take? No time at all! How long do the deletions take? Worst case: O(n 2 )  What algorithm is this? a.Insertion Sort b.Selection Sort c.Heap Sort d.Merge Sort e.None of these PQResult

14 “PQSort” insertions with Sorted List MAX-PQ PQ PQ PQ PQ

15 “PQSort” insertions with Sorted List MAX-PQ PQ How long does “build” take? Worst case: O(n 2 )  How long do the deletions take? What algorithm is this? a.Insertion Sort b.Selection Sort c.Heap Sort d.Merge Sort e.None of these

16 “PQSort” Build with Heap MAX-PQ PQ Floyd’s Algorithm Takes only O(n) time!

17 “PQSort” deleteMaxes with Heap MAX-PQ PQ PQ PQ PQ Totally incomprehensible as an array!

18 “PQSort” deleteMaxes with Heap MAX-PQ

19 “PQSort” deleteMaxes with Heap MAX-PQ Build Heap Note: 9 ends up being perc’d down as well since its invariant is violated by the time we reach it.

20 “PQSort” deleteMaxes with Heap MAX-PQ

21 “PQSort” with Heap MAX-PQ 21 How long does “build” take? Worst case: O(n) How long do the deletions take? Worst case: O(n lg n) What algorithm is this? a.Insertion Sort b.Selection Sort c.Heap Sort d.Merge Sort e.None of these PQResult

22 “PQSort” Sort(elts): pq = new PQ for each elt in elts: pq.insert(elt); sortedElts = new array of size elts.length for i = 0 to elements.length – 1: sortedElts[i] = pq.deleteMin return sortedElts 22 What sorting algorithm is this? a.Insertion Sort b.Selection Sort c.Heap Sort d.Merge Sort e.None of these

23 To Do Homework! Read: Epp Section 9.5 and KW Section 10.1, 10.4, and

24 Coming Up More sorting! Midterm (Feb 15 th ) 24


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